A planet revolves round the sun. Its velocity at the nearest point, distance $d_{1}$ from sun, is $v_{1}$ . The velocity of the planet at the farther point distance $d_{2}$ from sun will be

\frac{d_{1}^{2} v_{1}}{d_{2}^{2}}

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\frac{d_{2} v_{1}}{d_{1}}

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\frac{d_{1} v_{1}}{d_{2}}

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\frac{d_{2}^{2} v_{1}}{d_{1}^{2}}

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Solution

The correct option is D $\frac{d_{1} v_{1}}{d_{2}}$
The angular momemtum of the planet is conserved i.e. $L = m v r$ is constant at all points.
Now, consider the angular momemtums of given scenarios when the planet is farthest, nearest to be $L_{f}, L_{a}$ respectively. So, $L_{f} = L_{a}$ .
Its also given that nearest distance is $d_{1},$ with velocity $v_{1}$ and the farthest distance is $d_{2}$ . Substituting the given values we get
$m v_{2} d_{2} = m v_{1} d_{1}$ solving this we get
$v_{2} = \frac{v_{1} d_{1}}{d_{2}}$

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A planet revolves round the sun. Its velocity at the nearest point, distance d1 from sun, is v1. The velocity of the planet at the farther point distance d2 from sun will be

A planet revolves round the sun. Its velocity at the nearest point, distance $d_{1}$ from sun, is $v_{1}$ . The velocity of the planet at the farther point distance $d_{2}$ from sun will be